Question: Rewrite as a simplified fraction. ${2.5\overline{92} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2592.9292...\\ 10x &= 25.9292...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2567}$ ${x = \dfrac{2567}{990}} \text{or} {2 \dfrac{587}{990}}$